Question

If one of the zeroes of the quadratic polynomial $f\left(x\right)=14x^2-42k^{2}x-9$ is negative of the other, find the value of $k$.

Answer 1

Given the roots of the polynomial $f\left(x\right)=14x^2-42k^{2}x-9$ are $\alpha$ and $-\alpha$,

i.e., The sum of the roots is $0$,

$⟹\frac{42k^2}{14}=0⟹k=0$